Rock physics inversion based on an optimized MCMC method

Rock physics inversion is to use seismic elastic properties of underground strata for predicting reservoir petrophysical parameters.The Markov chain Monte Carlo(MCMC)algorithm is commonly used to solve rock physics inverse problems.However,all the parameters to be inverted are iterated simultaneously in the conventional MCMC algorithm.What is obtained is an optimal solution of combining the petrophysical parameters with being inverted.This study introduces the alternating direction(AD)method into the MCMC algorithm(i.e.the optimized MCMC algorithm)to ensure that each petrophysical parameter can get the optimal solution and improve the convergence of the inversion.Firstly,the Gassmann equations and Xu-White model are used to model shaly sandstone,and the theoretical relationship between seismic elastic properties and reservoir petrophysical parameters is established.Then,in the framework of Bayesian theory,the optimized MCMC algorithm is used to generate a Markov chain to obtain the optimal solution of each physical parameter to be inverted and obtain the maximum posterior density of the physical parameter.The proposed method is applied to actual logging and seismic data and the results show that the method can obtain more accurate porosity,saturation,and clay volume.

Azimuthally pre-stack seismic inversion for orthorhombic anisotropy driven by rock physics

Based on the long-wavelength approximation,a set of parallel vertical fractures embedded in periodic thin interbeds can be regarded as an equivalent orthorhombic medium. Rock physics is the basis for constructing the relationship between fracture parameters and seismic response. Seismic scattering is an effective way to inverse anisotropic parameters. In this study,we propose a reliable method for predicting the Thomsen's weak anisotropic parameters and fracture weaknesses in an orthorhombic fractured reservoir using azimuthal pre-stack seismic data. First, considering the influence of fluid substitution in mineral matrix, porosity, fractures and anisotropic rocks, we estimate the orthorhombic anisotropic stiffness coefficients by constructing an equivalent rock physics model for fractured rocks. Further, we predict the logging elastic parameters, Thomsen's weak parameters, and fracture weaknesses to provide the initial model constraints for the seismic inversion. Then, we derive the P-wave reflection coefficient equation for the inversion of Thomsen's weak anisotropic parameters and fracture weaknesses.Cauchy-sparse and smoothing-model constraint regularization taken into account in a Bayesian framework, we finally develop a method of amplitude variation with angles of incidence and azimuth(AVAZ) inversion for Thomsen's weak anisotropic parameters and fracture weaknesses, and the model parameters are estimated by using the nonlinear iteratively reweighted least squares(IRLS) strategy. Both synthetic and real examples show that the method can directly estimate the orthorhombic characteristic parameters from the azimuthally pre-stack seismic data, which provides a reliable seismic inversion method for predicting Thomsen's weak anisotropic parameters and fracture weaknesses.